Abstract:
Because Pi Day fell on the Friday before break, many of you
may have missed out on the festivities. We’ll develop a bit of
integral geometry (a.k.a. geometric probability) that lets us compute
Pi by a random process – the Buffon Needle Problem – as well as the
lengths of curves in the plane and the sphere, eventually leading to
the now-classic theorem of Fenchel-Fary-Milnor about the total
curvature of space curves.